Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x + 5$ and $ JT = 6x + 11$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x + 5} = {6x + 11}$ Solve for $x$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({6}) + 5$ $ JT = 6({6}) + 11$ $ CJ = 42 + 5$ $ JT = 36 + 11$ $ CJ = 47$ $ JT = 47$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {47} + {47}$ $ CT = 94$